The invention provides a CuCe-SAPO-34 molecular sieve catalyst, as well as a preparation method and use thereof. The method comprises the following steps: adding pseudo-boehmite in deionized water, stirring, then adding ortho-phosphoric acid and fumed silica, uniformly mixing, then adding copper salt and tetraethylenepentamine, sufficiently mixing, adding cerate and n-propylamine, loading the completely mixed gel in a hydrothermal reaction kettle to crystallize, cooling at room temperature, separating the solid crystallized product from the mother liquor, washing to neutral, drying, and roasting in air to obtain the CuCe-SAPO-34 molecular sieve catalyst. The CuCe-SAPO-34 molecular sieve catalyst is prepared through the adoption of the hydrothermal synthesis method, and the molecular sieve catalyst with excellent NH3-SCR catalytic activity and water resistance is obtained by adjusting the loading amount of cerium through the control of the input of the cerate.